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 A035604 Number of points of L1 norm 10 in cubic lattice Z^n. 3
 0, 2, 40, 402, 2720, 14002, 58728, 209762, 658048, 1854882, 4780008, 11414898, 25534368, 53972178, 108568488, 209070018, 387328512, 693230658, 1202893992, 2029779538, 3339504032, 5369283570, 8453107432, 13053926690, 19804348032, 29557550050, 43450388072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf). M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - N. J. A. Sloane, Feb 13 2013 M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5. Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44. FORMULA a(n) = 2n^2/14175 * (2n^8 + 120n^6 + 1806n^4 + 7180n^2 + 5067). G.f.: 2*x*(1+x)^9/(1-x)^11. - Colin Barker, Apr 15 2012 a(n) = 2*A099197(n). - R. J. Mathar, Dec 10 2013 a(n) = a(n-1) + A035603(n) + A035603(n-1). - Bruce J. Nicholson, Mar 11 2018 MAPLE f := proc(d, m) local i; sum( 2^i*binomial(d, i)*binomial(m-1, i-1), i=1..min(d, m)); end; # n=dimension, m=norm MATHEMATICA f[d_, m_] := Sum[2^i*Binomial[d, i]*Binomial[m-1, i-1], {i, 1, Min[d, m]}]; a[n_] := f[n, 10]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Nov 24 2017, from Maple *) PROG (PARI) x='x+O('x^99); concat(0, Vec(2*x*(1+x)^9/(1-x)^11)) \\ Altug Alkan, Mar 12 2018 CROSSREFS Cf. A035607. Sequence in context: A155977 A092698 A181175 * A180429 A108033 A160229 Adjacent sequences:  A035601 A035602 A035603 * A035605 A035606 A035607 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 26 09:32 EDT 2020. Contains 334620 sequences. (Running on oeis4.)